MOND: variable gravity strength
Oz
John Baez <ba...@galaxy.ucr.edu> writes in another thread:
>http://www.astro.umd.edu/~ssm/mond/faq.html
[Ta, sir wiz, some extracts below.]
[I have switched equations to spr-speak]
I have a question at the end.
=============================
Q: What is the modification?
A: MOND can be interpreted as either a modification of gravity through a
change to the Poisson equation, or as a modification of inertia through
a breaking of the equivalence of inertial and gravitational mass.
The modification occurs at very small accelerations. Above a critical
acceleration a_0 (the one parameter of the theory), everything is
normal.
Below a_0, the effective acceleration approaches a = (g_N a_0)^1/2,
where g_N is the normal Newtonian acceleration.
The two regimes are joined smoothly by an interpolation function mu(x)
with the asymptotic property mu(x) -> 1 for x >> 1 and mu(x) -> x for x
<< 1, where x = a/a_0.
In the case of a modification of the Law of Inertia, a=F/m becomes
a=F/[m*mu(x)], and the effective acceleration can be found from
a*mu(x) = g_N.
In the case of a modification of the Law of Gravity, the Poisson
equation becomes
del.[mu(|del_phi|/a_0)del_phi] = 4 pi G rho
which is well approximated by a*mu(x) = g_N.
Q: What is mu(x)?
A: The interpolation function is not specified theoretically, but there
is a fairly narrow range of empirically acceptable mu(x). Two commonly
assumed forms which are acceptable to galaxy data are
mu(x) = x(1+x^2)^(-1/2) and mu(x) = 1-e^(-x).
Q: What is the acceleration scale?
A: a_0 = 1.2 x 10-10 m s-2, i.e., about one Angstrom per second per
second. This is one part in 10^11 of what we feel on the surface of the
earth. The precise value depends on the distance scale to galaxies, so
perhaps it would be better to say a_0 = 1.2 x 10^(-10) m s-2 (h_75)^2,
where h = H0/75 is the Hubble Constant (the expansion rate of the
universe) in units of H0 = 75 km s-1 Mpc-1. (Currently, most
measurements report values in the neighborhood of H0 = 70 +/- 7 km s-1
Mpc-1.)
Q: MOND fits the rotation curves of spiral galaxies well, but it was
designed to do that. So do such data provide any test?
A: Yes.
That MOND was "designed" to fit rotation curves and is therefore
guaranteed to do so is a common misconception.
Both MOND and dark matter were invented to explain the presence of mass
discrepancies in astronomical data, especially the flat rotation curves
of spiral galaxies.
It is often asserted that MOND is ad hoc (and therefore bad), but this
is also true of dark matter. Once invoked, dark matter can be
distributed in any way necessary to explain just about anything. It is
difficult to test, and does not constitute a falsifiable theory. In
contrast, once a modified force law is specified, there is no freedom to
adjust its predictions.
MOND can not fit any arbitrary rotation curve: it is tied down by the
observed mass distribution. However, it does fit real data. I find it
remarkable that of the infinite variety of things rotation curves might
plausibly do were they caused by a Newtonian disk + dark matter halo,
they in fact do the one (and only one) thing allowed by MOND.
Fundamental Clue or Big Cosmic Accident? (Is God subtle or malicious?)
MOND's detractor's often assert it is just some sort of fluke, so I
guess they prefer to believe that God is malicious.
=================================================
OK, my question:
Generally, 'constants' in astronomical large scales seem to be evaluated
from a model, and deviations from the model suggesting variations in the
'constants'. So the information from the most recent u-wave background
data, where they confidently give amounts of negative energy and dark
matter in the universe are presumably based on GR and QM. Were, for
example, you to use a MOND-like model then you would come to different
conclusions. The universe would have a different age and expected
distributions of matter would be different, thus requiring different
amounts of unobserved exotics. Is this a fair comment?
I note from the mond page that nobody has yet managed a reasonable
merging of GR and mond, not least because it implies that inertia and
mass are NOT precisely equivalent. I'm thus not expecting proper answers
but would hope for some general pointers with ample handwaving.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
Note: soon (maybe already) only posts via despammed.com will be accepted.
Douglas B Sweetser
At this point, I believe MOND has nothing to do with dark energy (which is
the same as a non-zero cosmological constant which is the same as
quintessence). The need for the dark energy is to make the big bang
solution stable. Otherwise, the initial conditions would have to be right
to some 50 significant digits, kind of like balancing a pencil on its tip
onto another pencil tip.
If MOND took the place of all the dark matter (which is not dark energy), I
believe that dark energy estimates would just expand to take its place.
Dark energy is about the big bang, how much stuff there was originally. 5%
is stuff we can see, the rest is mystery meat.
Thanks for the quotes from the FAQ. The MOND group likes how there is only
one additional constant to the Universe to make it work, the a0
acceleration scale. Yet the FAQ points out they are guessing functions for
how the transition happens. That cannot be pleasing work. It is sooo much
better when all function flow from fundamental understanding.
> I note from the mond page that nobody has yet managed a reasonable
> merging of GR and mond, not least because it implies that inertia and
> mass are NOT precisely equivalent.
This was insightful! We have very good experimental data that inertial
mass is equavalent to gravitational mass. We have fun thought experiments
to the same point. We have grand equations the arise only because inertial
and gravitational mass are treated exactly equally. If you want to know
why MOND with more numerical success than its direct compeditor dark matter
has not caught on, perhaps this gap is the reason - there is no clear
reason why the equivalence principle should break for low accelerations.
For a review of current works in progress circa 2001, including a report
card, go here:
http://www.sciam.com/print_version.cfm?
articleID=000BCF6F-22B7-1C71-84A9809EC588EF21
doug
quaternions.com
eb...@lfa221051.richmond.edu
Douglas B Sweetser <swee...@TheWorld.com> wrote:
>At this point, I believe MOND has nothing to do with dark energy (which is
>the same as a non-zero cosmological constant which is the same as
>quintessence). The need for the dark energy is to make the big bang
>solution stable. Otherwise, the initial conditions would have to be right
>to some 50 significant digits, kind of like balancing a pencil on its tip
>onto another pencil tip.
I know of no sense in which this is true. People have in the past
made "fine-tuning" arguments of the sort you describe in favor of
particular values of particular cosmological parameters, but dark
energy is not an example of this. People started to believe in dark
energy because observations led them there, not because of fine-tuning
arguments. In fact, dark-energy models do somewhat badly by the
fine-tuning standard, as they require that we live at a special epoch,
in which the densities of matter and dark energies are roughly
comparable.
To be a bit more specific, people believe in dark energy mostly because
there is observational evidence in favor of the following
statements:
1. The Universe is spatially flat. (The evidence for this comes
mostly from observations of the microwave background radiation.)
2. The density of matter (visible and dark) is much less than the
critical density. Many different lines of evidence have been
converging on this conclusion for a long time.
3. Observations of high-redshift supernovae are not consistent with an
expansion rate that is slowing down at the rate expected for a
matter-dominated Universe.
Points 1 and 2 must be combined before they can be taken as evidence
of dark energy, of course. Point 3 is a separate line of argument.
The fact that two completely different lines of argument, which probe
very different aspects of the physics, point to the same conclusion is
highly suggestive that we're on the right track.
>If MOND took the place of all the dark matter (which is not dark energy), I
>believe that dark energy estimates would just expand to take its place.
I don't know how to evaluate this statement. The problem is that MOND
is not a model. That is, it doesn't specify the underlying physics
in a way that allows one to make predictions. So as far as I know
there is no clear way to complete almost any sentence that
begins "If MOND ..."
For instance, there's no clear way to reconcile MOND with general
relativity, but general relativity is essential to the interpretation
of all large-scale cosmological observations. So, for instance,
there's no sensible way to predict what the spectrum of microwave
background fluctuations should look like in MOND. Nor is there any
clear MOND prediction for the high-redshift supernova data. Since
these are the main lines of evidence for dark energy, I don't think
there can be any justification for your guess about the role of dark
energy in MOND.
>This was insightful! We have very good experimental data that inertial
>mass is equavalent to gravitational mass. We have fun thought experiments
>to the same point. We have grand equations the arise only because inertial
>and gravitational mass are treated exactly equally. If you want to know
>why MOND with more numerical success than its direct compeditor dark matter
>has not caught on, perhaps this gap is the reason - there is no clear
>reason why the equivalence principle should break for low accelerations.
I can't imagine any way the phrase "with more numerical success than
its direct competitor" can be justified. The hallmark of a successful
theory is that it make correct predictions for phenomena other than
those it was originally postulated to solve. As far as I know, MOND's
score by that standard is precisely zero.
-Ted
--
[E-mail me at na...@domain.edu, as opposed to na...@machine.domain.edu.]
Oz
>Hello Oz:
>
>At this point, I believe MOND has nothing to do with dark energy (which is
>the same as a non-zero cosmological constant which is the same as
>quintessence). The need for the dark energy is to make the big bang
>solution stable. Otherwise, the initial conditions would have to be right
>to some 50 significant digits, kind of like balancing a pencil on its tip
>onto another pencil tip.
I'm not entirely sure you can say that. The BB currently requires GR, as
I understand it, unless you are discussing models that use inflation.
Inflation is, as I understand it, pretty well put in by hand.
>If MOND took the place of all the dark matter (which is not dark energy), I
>believe that dark energy estimates would just expand to take its place.
>Dark energy is about the big bang, how much stuff there was originally. 5%
>is stuff we can see, the rest is mystery meat.
I'm not so sure. Mond operates at very low accelerations, I don;t think
the early stages of the BB were low acceleration regimes. Too much
matter, too close together, for that.
My point is more that the estimates for dark matter and for dark energy
require the use of models (generally GR + DM & DE put in by hand) that
depend on the DE & DM. Obviously if gravity doesn't quite behave the way
we think it does at low accelerations then the model is inaccurate. For
example we shouldn't use large amounts of dark matter in the model if it
isn't there. If we don't include it then gravitational forces will be
less (less matter) but then at low accelerations it will be more due to
mond. Consequently the model behaves differently. For example if (in
effect) gravity is stronger for the interactions of distant bodies
(mond) then the more recent phase of expansion dominated by galactic
clusters (say) have a stronger gravitational attraction than we would
have thought so they will initially have had a higher initial velocity.
I *think* that means they will have taken less time to arrive at the
universe we see, and should be slowing more quickly than we think. Hard
to see this as the information will only arrive over the next few
1,000,000 years.
Equally we wouldn't need dark energy to 'explain' extra expansion if a
model with mond doesn't give us extra acceleration. I think a stronger
gravity at low accelerations might fix this when used in a model, there
again maybe not.
So my question asks what gross effects mond would have on the evolution
of the universe. Probably need to be done crudely by computer.
>Thanks for the quotes from the FAQ. The MOND group likes how there is only
>one additional constant to the Universe to make it work, the a0
>acceleration scale. Yet the FAQ points out they are guessing functions for
>how the transition happens. That cannot be pleasing work. It is sooo much
>better when all function flow from fundamental understanding.
It's a curve-fitting exercise. No more. That;s how QM was derived.
>> I note from the mond page that nobody has yet managed a reasonable
>> merging of GR and mond, not least because it implies that inertia and
>> mass are NOT precisely equivalent.
>
>This was insightful! We have very good experimental data that inertial
>mass is equavalent to gravitational mass.
Not over the scales mond applies to.
>We have fun thought experiments
>to the same point. We have grand equations the arise only because inertial
>and gravitational mass are treated exactly equally. If you want to know
>why MOND with more numerical success than its direct compeditor dark matter
>has not caught on, perhaps this gap is the reason - there is no clear
>reason why the equivalence principle should break for low accelerations.
So? There is no clear reason why QM works.
It just does. That is enough.
I'm more interested in whether it is still giving sensible answers for
even bigger structures. Clusters of galaxies and superclusters. Then
using it's effects to track the universe back in time and seeing if that
gives reasonable results. If these fail, then mond is an interesting
numerical exercise, no more. If they don;t look unreasonable then it
looks more plausible.
Oz
>I can't imagine any way the phrase "with more numerical success than
>its direct competitor" can be justified.
That's probably fair, but much less needs to be put in by hand.
Just the one a_0, which is the same for all galaxies.
>The hallmark of a successful
>theory is that it make correct predictions for phenomena other than
>those it was originally postulated to solve. As far as I know, MOND's
>score by that standard is precisely zero.
I don;t think anyone would suggest it was a theory in the sense of
predicting changes in basic physics. It's a curve-fitting that works, if
it turned out to be little more than a convenient artefact then that's
life.
However it was apparently first developed rather a long time ago when
very few galaxies had their rotations measured. So far, and with no
alteration of a_0 it has matched all the galaxies measured including
some odd very large (physically) low mass ones. That counts as usefully
predictive in my book.
To me at least a proposal that continues to work as more and more
objects are measured with rather different physical characteristics
while competing theories just put in parameters by hand to fit on an
individual ad-hoc basis warrants *some* investigation.
In particular, as I said before, it should apply to galactic clusters
and superclusters. If it doesn't then there is a flaw, if it does then
that's a heck of a range of objects following the 'law'.
Another test would calculate (roughly) the 'mond' age of the universe
because mond uses a different force law, although currently matched by
dark matter in conventional models. Hmm, I guess it would mean that the
early universe would contain less matter and so would expand more
rapidly. Assuming that the existing movements are equally well described
by both dark matter and mond one imagines that the predictions for 'more
recent times' would be comparable. I think an even younger universe than
current models is not what the doctor ordered, although I am prone to
getting things horrible wrong.
eb...@lfa221051.richmond.edu
Oz <ozac...@despammed.com> wrote:
>eb...@lfa221051.richmond.edu writes
>>I can't imagine any way the phrase "with more numerical success than
>>its direct competitor" can be justified.
>That's probably fair, but much less needs to be put in by hand.
>Just the one a_0, which is the same for all galaxies.
I haven't looked at the data recently, but I find it hard to believe
that you can fit all rotation curves with a single parameter. Galaxy
rotation curves are complicated! Many are approximately flat, but a
significant fraction aren't.
But I'm not an expert in this field. I'd be interested to hear
from people who actually work on galaxy rotation curves. I added
sci.astro.research to the Newsgroups line in the hope of
catching the attention of such people.
>Another test would calculate (roughly) the 'mond' age of the universe
>because mond uses a different force law, although currently matched by
>dark matter in conventional models.
This is the sort of thing I was talking about when I said before that
MOND is not a model. As far as I know, there is simply no way to
generate a MOND prediction for the age of the Universe. There is no
MOND version of the Friedmann equation (the equation that describes
the way the expansion rate evolves over time), because the Friedmann
equation is based on general relativity. MOND is inconsistent
with general relativity and doesn't replace it with anything else.
The same problem arises with nearly all cosmological observables.
John Baez
Oz <ozac...@despammed.com> wrote approximately:
>Generally, 'constants' in astronomical large scales seem to be evaluated
>from a model, and deviations from the model suggesting variations in the
>'constants'.
Right.
>So the information from the most recent microwave background
>data, where they confidently give amounts of negative energy and dark
>matter in the universe are presumably based on GR and QM.
Right.
Of course, even assuming the existence of dark energy
(aka a nonzero cosmological constant) is stretching GR a tiny bit;
originally GR didn't have a cosmological constant. But now
people stick it in as a free parameter, along with the Hubble
constant and the densities of various sorts of matter, and see
which values seem to fit the data best.
QM comes into this only rather indirectly, e.g. in our models of
stellar evolution, which require that we understand nuclear fusion.
>Were, for example, you to use a MOND-like model then you would come
>to different conclusions.
Now for my real point:
Alas, as Ted Bunn has pointed out, there is no "MOND-like big bang
model", so we can't do this. At least, not yet.
The usual big bang model is derived from the equations of general
relativity. As the name suggests, MOND (Modified Newtonian Dynamics)
is a modified version of Newtonian gravity, not general relativity...
so while it's good enough for describing how stuff orbits galaxies,
it's not good enough for describing the big bang.
Of course, a real MOND afficionado should take this as a challenge
and try to whip up a modified version of GR that yields MOND rather
than Newtonian gravity in the nonrelativistic limit - low speeds,
weak gravitational fields.
The MOND FAQ mentions two attempts:
1988, Physics Letters B202, 497
Jacob D. Bekenstein
Phase Coupled Gravitation and Gauge Fields
1997, ApJ, 480, 492
Sanders, R. H.
A Stratified Framework for Scalar-Tensor Theories of Modified Dynamics
http://xxx.lanl.gov/abs/astro-ph/9612099
I don't know anything about them. But, if someone put serious effort
into them, perhaps they could see how (and if!) the big bang model
works in these alternate theories.
Until someone does, most cosmologists won't take MOND seriously -
not merely out of prejudice, but because it makes no predictions
about the large-scale dynamics of the universe.
Chris Mihos
> In article <b45jnb$2ut$1...@lfa222122.richmond.edu>,
> Oz <ozac...@despammed.com> wrote:
>>eb...@lfa221051.richmond.edu writes:
>>>I can't imagine any way the phrase "with more numerical success than
>>>its direct competitor" can be justified.
>>That's probably fair, but much less needs to be put in by hand.
>>Just the one a_0, which is the same for all galaxies.
> I haven't looked at the data recently, but I find it hard to believe
> that you can fit all rotation curves with a single parameter. Galaxy
> rotation curves are complicated! Many are approximately flat, but a
> significant fraction aren't.
Well, of course, fitting MOND to a rotation curve isn't a single
parameter fit. there's a0, yes, but there's also the stellar mass to
light ratio, the gas content (and its uncertain helium correction), and
the distance (which plays into the derived value of a0). There are fewer
free parameters than w/ dark matter, yes, but it's not just one free
parameter.
> But I'm not an expert in this field. I'd be interested to hear
> from people who actually work on galaxy rotation curves. I added
> sci.astro.research to the Newsgroups line in the hope of
> catching the attention of such people.
Look at work by Stacy McGaugh and Erwin deBlok (and their
collaborators). In fact, Stacy has a very useful (and often amusing) web
of MOND links online at http://www.astro.umd.edu/~ssm/mond/
--chris
Douglas B Sweetser
> I can't imagine any way the phrase "with more numerical success than
> its direct competitor" can be justified. The hallmark of a successful
> theory is that it make correct predictions for phenomena other than
> those it was originally postulated to solve. As far as I know, MOND's
> score by that standard is precisely zero.
MOND did score such a success with something called low-surface-brightness
galaxies. As the name implies, they are hard to see. At the time Milgrom
published his work, he made a prediction about the amount of mass that
would appear to be "missing" but would be explained by MOND.
Later observations confirmed his predictions. It was this story that most
impressed me about the proposal. I also liked that it dependend on only
one parameter. Folks who work with dark matter appear to have considerably
more freedom. Have dark matter workers predicted anything (I don't know)?
That said, MOND is not a proposal with a rational theoretical foundation.
That means it is difficult to fit into our current rational foundation of
the big bang in a precise way. I was guilty of hand waving. I am a fan of
its numerical success with limited parameters, nothing more.
doug
quaternions.com
John Baez
Douglas B Sweetser <swee...@TheWorld.com> wrote:
>The need for the dark energy is to make the big bang
>solution stable. Otherwise, the initial conditions would have to be right
>to some 50 significant digits, kind of like balancing a pencil on its tip
>onto another pencil tip.
Eh? I don't know about that! All I know is that dark energy
(i.e. a positive cosmological constant) is currently the most
conservative way to explain the apparent acceleration in the
expansion of the universe.
Oz
>>Oz wittered
>>So the information from the most recent microwave background
>>data, where they confidently give amounts of negative energy and dark
>>matter in the universe are presumably based on GR and QM.
>
>Right.
>
>Of course, even assuming the existence of dark energy
>(aka a nonzero cosmological constant) is stretching GR a tiny bit;
>originally GR didn't have a cosmological constant. But now
>people stick it in as a free parameter, along with the Hubble
>constant and the densities of various sorts of matter, and see
>which values seem to fit the data best.
>
>>Were, for example, you to use a MOND-like model then you would come
>>to different conclusions.
>
>Now for my real point:
>
>Alas, as Ted Bunn has pointed out, there is no "MOND-like big bang
>model", so we can't do this. At least, not yet.
>
>The usual big bang model is derived from the equations of general
>relativity. As the name suggests, MOND (Modified Newtonian Dynamics)
>is a modified version of Newtonian gravity, not general relativity...
>so while it's good enough for describing how stuff orbits galaxies,
>it's not good enough for describing the big bang.
Indeed.
It would have to be modified. Initially in a quick-and-dirty numerical
way using the many powerful tools available foc to academics. From my
position of infinite ignorance I would imagine two proposals that would
seem plausible.
1) Is to simply add (by hand) an extra mond-force whilst allowing GR to
continue warping spacetime in the usual way. Obviously you may want to
include the pressure due to the mond-force. I would expect this to be
'relatively simple'.
2) To recast GR to mimic mond. I would expect this to be mindblowingly
difficult and wouldn't advise it even for an expert. The implication of
separating inertial and gravitation mass and arranging a force law that
looks more like the strong force would probably result in brain damage.
Of course it's dead easy to say this when you are infinitely ignorant.
>Of course, a real MOND afficionado should take this as a challenge
>and try to whip up a modified version of GR that yields MOND rather
>than Newtonian gravity in the nonrelativistic limit - low speeds,
>weak gravitational fields.
I get the feeling that there aren't many afficionado's prepared to put
serious effort into what is simply a curve-fitting exercise that appears
to be unreasonably accurate.
Whilst success may well bring fame and fortune, failure gets you nothing
but wasted years. Scientists these days seem to prefer small advances
guaranteed to give success (or dropped before too much time is lost)
rather than spend years on speculative work. Pretty sensible of them
really. It would probably be someone in a real job, playing with
something he enjoys, or a near-retired tenured prof dabbling for fun.
>The MOND FAQ mentions two attempts:
>
>1988, Physics Letters B202, 497
>Jacob D. Bekenstein
>Phase Coupled Gravitation and Gauge Fields
>
>1997, ApJ, 480, 492
>Sanders, R. H.
>A Stratified Framework for Scalar-Tensor Theories of Modified Dynamics
>http://xxx.lanl.gov/abs/astro-ph/9612099
>
>I don't know anything about them. But, if someone put serious effort
>into them, perhaps they could see how (and if!) the big bang model
>works in these alternate theories.
Probably. I doubt I would follow them past the third word.
>Until someone does, most cosmologists won't take MOND seriously -
>not merely out of prejudice, but because it makes no predictions
>about the large-scale dynamics of the universe.
And there you have it. Chicken and egg .....
eb...@lfa221051.richmond.edu
In article <b4b3hi$56f$1...@lfa222122.richmond.edu>,
Oz <ozac...@despammed.com> wrote:
>It would have to be modified. Initially in a quick-and-dirty numerical
>way using the many powerful tools available foc to academics. From my
>position of infinite ignorance I would imagine two proposals that would
>seem plausible.
>
>1) Is to simply add (by hand) an extra mond-force whilst allowing GR to
>continue warping spacetime in the usual way. Obviously you may want to
>include the pressure due to the mond-force. I would expect this to be
>'relatively simple'.
I really don't think there's any sensible way to do this. MOND is
radically non-relativistic: the differences between MOND and ordinary
dynamics can't, as far as I can see, be cast in a form that could be
plugged into general relativity in a consistent way, even
approximately.
The point is that MOND breaks general covariance, which is the
property of general relativity that says that you can do things
equally well in all coordinate systems. Once you give that up, it's
hard to say anything sensible using general relativity.
>2) To recast GR to mimic mond. I would expect this to be mindblowingly
>difficult and wouldn't advise it even for an expert. The implication of
>separating inertial and gravitation mass and arranging a force law that
>looks more like the strong force would probably result in brain damage.
I don't understand the last sentence, but I agree with the one before
it: this looks like a difficult job! I personally have no idea
how to do it.
Oz
>
>In article <b4b3hi$56f$1...@lfa222122.richmond.edu>,
>Oz <ozac...@despammed.com> wrote:
>
>>It would have to be modified. Initially in a quick-and-dirty numerical
>>way using the many powerful tools available foc to academics. From my
>>position of infinite ignorance I would imagine two proposals that would
>>seem plausible.
>>
>>1) Is to simply add (by hand) an extra mond-force whilst allowing GR to
>>continue warping spacetime in the usual way. Obviously you may want to
>>include the pressure due to the mond-force. I would expect this to be
>>'relatively simple'.
>
>I really don't think there's any sensible way to do this. MOND is
>radically non-relativistic: the differences between MOND and ordinary
>dynamics can't, as far as I can see, be cast in a form that could be
>plugged into general relativity in a consistent way, even
>approximately.
OK.
Is it possible to see how it matches clusters of galaxies in the same
way it matches various galaxy rotation curves? I take mihos' comments
that there are a lot of unknown, or probably more likely poorly known,
parameters in working out the amount and distribution of dark matter but
presumably there are at least reasonable estimates for most of these. I
imagine that reasonable estimates of neutral gas and other 'known but
dark' matter are available.
Obviously if mond works tolerably well at even these scales then I would
suggest ignoring it might not be that smart. If, on the other hand, it
fails dismally then we can all breath a sigh of relief.
>The point is that MOND breaks general covariance, which is the
>property of general relativity that says that you can do things
>equally well in all coordinate systems. Once you give that up, it's
>hard to say anything sensible using general relativity.
I'll take your word for it. However what would you do if it DID turn out
to be right? Give up and become a schoolteacher? No, you would just
dream up tools that could cope with it to first order at least.
>>2) To recast GR to mimic mond. I would expect this to be mindblowingly
>>difficult and wouldn't advise it even for an expert. The implication of
>>separating inertial and gravitation mass and arranging a force law that
>>looks more like the strong force would probably result in brain damage.
>
>I don't understand the last sentence,
Well, assuming I have it right it says that gravity for low
accelerations stays at a constant low force. This looks to me quite
'similar' to the strong force that also stays the same at long
distances. If, for example, I had a system that exhibited only very low
accelerations (ie newtonian gravity was negligible) and tried to remove
a star to infinity I think mond would say that it required an infinite
amount of energy.
>but I agree with the one before
>it: this looks like a difficult job! I personally have no idea
>how to do it.
Woah! That's *scary*!
Oz
>In article <b4b3hi$56f$1...@lfa222122.richmond.edu>,
>Oz <ozac...@despammed.com> wrote:
>>It would have to be modified. Initially in a quick-and-dirty numerical
>>way using the many powerful tools available foc to academics. From my
>>position of infinite ignorance I would imagine two proposals that would
>>seem plausible.
>>
>>1) Is to simply add (by hand) an extra mond-force whilst allowing GR to
>>continue warping spacetime in the usual way. Obviously you may want to
>>include the pressure due to the mond-force. I would expect this to be
>>'relatively simple'.
>I really don't think there's any sensible way to do this. MOND is
>radically non-relativistic: the differences between MOND and ordinary
>dynamics can't, as far as I can see, be cast in a form that could be
>plugged into general relativity in a consistent way, even
>approximately.
OK.
Is it possible to see how it matches clusters of galaxies in the same
way it matches various galaxy rotation curves? I take mihos' comments
that there are a lot of unknown, or probably more likely poorly known,
parameters in working out the amount and distribution of dark matter but
presumably there are at least reasonable estimates for most of these. I
imagine that reasonable estimates of neutral gas and other 'known but
dark' matter are available.
Obviously if mond works tolerably well at even these scales then I would
suggest ignoring it might not be that smart. If, on the other hand, it
fails dismally then we can all breath a sigh of relief.
>The point is that MOND breaks general covariance, which is the
>property of general relativity that says that you can do things
>equally well in all coordinate systems. Once you give that up, it's
>hard to say anything sensible using general relativity.
I'll take your word for it. However what would you do if it DID turn out
to be right? Give up and become a schoolteacher? No, you would just
dream up tools that could cope with it to first order at least.
>>2) To recast GR to mimic mond. I would expect this to be mindblowingly
>>difficult and wouldn't advise it even for an expert. The implication of
>>separating inertial and gravitation mass and arranging a force law that
>>looks more like the strong force would probably result in brain damage.
>I don't understand the last sentence,
Well, assuming I have it right it says that gravity for low
accelerations stays at a constant low force. This looks to me quite
'similar' to the strong force that also stays the same at long
distances. If, for example, I had a system that exhibited only very low
accelerations (ie newtonian gravity was negligible) and tried to remove
a star to infinity I think mond would say that it required an infinite
amount of energy.
>but I agree with the one before
>it: this looks like a difficult job! I personally have no idea
>how to do it.
Woah! That's *scary*!
robert bristow-johnson
John (or anyone else), can you comment more on this? i had always been
disturbed by the apparently fully accepted finding that the rate of
expansion of the universe is increasing in time. this "dark energy" thing
can explain it a bit *for*now*, but doesn't the conservation of energy and
mass (or the sum of the two when the appropriate scaler, c^2, is used to
convert between them) still apply to our universe, if considered to be a
closed system? or is the universe not closed? or is the conservation of
energy and mass tossed onto the scrap heap along with newtonian mechanics
and other anachronisims?
where is this energy, dark or not, coming from that feeds this accelerating
expansion?
just curious.
Steve Carlip
> The problem is that MOND
> is not a model. That is, it doesn't specify the underlying physics
> in a way that allows one to make predictions. So as far as I know
> there is no clear way to complete almost any sentence that
> begins "If MOND ..."
People following this thread ight want to look at two papers on
the difficulties of extending MOND to large scales:
Cosmological Difficulties with Modified Newtonian Dynamics
(or: La Fin du MOND?), D. Scott et al., astro-ph/0104435
Astrophysical Constraints on Modifying Gravity at Large Distances,
A. Aguirre et al., hep-ph/0105083
Steve Carlip
John Baez
>From my
>position of infinite ignorance I would imagine two proposals that would
>seem plausible.
>
>1) Is to simply add (by hand) an extra mond-force whilst allowing GR to
>continue warping spacetime in the usual way. Obviously you may want to
>include the pressure due to the mond-force. I would expect this to be
>'relatively simple'.
I can't think of a way to do this that doesn't make me feel nauseated.
The equations of general relativity hold in any coordinate system.
But you can't throw in an extra sort of "MOND-force" in a coordinate-free
way, since this force acts instantaneously at a distance, and you need
to pick coordinates to define what "instantaneous" means. This is why
Einstein threw out Newtonian gravity after he came up with special
relativity.
In theory, I could hold my nose and say "I'll take this one
special sort of solution of Einstein's equations, the Friedman-
Robertson-Walker big bang solution, where I do have a special
time coordinate, namely "cosmic time", and I'll use that time
coordinate to define an extra "MOND-force" which acts instantaneously
at a distance, and see how this affects things."
In practice, I just wouldn't have the stomach to do this sort of thing.
I suppose some physicists would, and it might actually be worthwhile!
It can be helpful, sometimes, to do something monstrously ugly that
you secretly hope is not ultimately correct, just in order to get a
little insight and maybe some new ideas. I'm just too much a slave
to elegance to do this here.
>2) To recast GR to mimic mond. I would expect this to be mindblowingly
>difficult and wouldn't advise it even for an expert.
I think this is what those 2 papers I cited were trying to do:
Don't throw in an extra "MOND-force" that acts instantaneously at
a distance. Instead, modify the Lagrangian and thus the field equations
of general relativity to get something that acts more "MOND-ish"!
You're right that this sounds mindblowingly difficult. But
it depends in part on how ugly you let the theory be! And
also how well you want it to work.
I get the impression that the 2 theories in question are a bit
ugly, and nobody knows for sure if they really work -
i.e., pass all the dozens of experimental tests that GR passes,
but also act sufficiently MOND-ish.
Someone should study these theories and report back. But it won't
be me - I have more fun things to do. If I were the Emperor of Physics,
I'd send out a team of 4 grad students and a professor to explore
in this direction. But I'm not.
Sociologically, the real problem with these theories is that they
aren't consequences of any sort of string or membrane theory.
If they were, you'd have 100 people working on them day and night,
and huge conferences on the subject.
Oz
robert bristow-johnson <r...@surfglobal.net> writes
>or is the conservation of
>energy and mass tossed onto the scrap heap along with newtonian mechanics
>and other anachronisims?
This is where I came in, many years ago.
In a long thread on sci.physics, ted bunn eventually put together an
argument that I found irrefutable. At that point I realised that my
world view was broken and I've been trying to catch up ever since.
In General Relativity the concept of total energy of the universe is
essentially undefined. Without a good global measure of 'total energy of
the universe' then how can it be considered conserved?
Fortunately it's still reasonably valid to have a local conservation of
energy. Be thankful for small mercies.
The thread is a long one, and pretty well permanently exhausted Ted, who
now (sensibly) quietly fades away after a few posts.
For further information see google on sci.physics or 'the GR tutorial
thread' on spr, or the wizards wonderful website (Baez homesite).
It's a great ride, and if I can follow it well enough, then so can your
dog.
Doug B Sweetser
> No, you would just
> dream up tools that could cope with it to first order at least.
This is what any new proposal must do in my opinion. Remember how the
Swiss high school teacher Balmer through trial and error came up with a
formula that worked for the spectral lines of hydrogen? That was only
explained by Bohr quantizing angular momentum. Even that was only a
partial explanation, needing Schrodinger's wave equation as its
justification. I think MOND has the right function for weak gravitational
systems. I don't think the reason for the change in the form of classical
gravity due to the weakness of the field - as weak as it is - stands any
chance of lasting (there is almost nothing there to stand the test of time).
doug
quaternions.com
Will Kinney
John Baez wrote:
> In article <b4b3hi$56f$1...@lfa222122.richmond.edu>,
> Oz <ozac...@despammed.com> wrote:
>>1) Is to simply add (by hand) an extra mond-force whilst allowing GR to
>>continue warping spacetime in the usual way. Obviously you may want to
>>include the pressure due to the mond-force. I would expect this to be
>>'relatively simple'.
>
>
> I can't think of a way to do this that doesn't make me feel nauseated.
This will probably not help with your gastric issues:
http://arxiv.org/ps/astro-ph/0006453
The idea is to add an extra force, along the lines suggested by Oz,
which couples to baryon number as a charge and has a logarithmic
potential. Turns out it gives you nice flat rotation curves and also
neatly matches cluster mass/light ratios without needing any dark
matter. It differs from MOND in that the model contains a fundamental
length scale instead of a fundamental acceleration scale. Where it fails
is gravitational lensing, since the force doesn't couple to photons, and
hence you expect that lensing mass estimates of clusters should come in
a factor of 10 or so low. They don't.
Enjoy your dinner.
-- Will
Oz
John Baez <ba...@galaxy.ucr.edu> writes
>In article <b4b3hi$56f$1...@lfa222122.richmond.edu>,
>Oz <ozac...@despammed.com> wrote:
>
>>From my
>>position of infinite ignorance I would imagine two proposals that would
>>seem plausible.
>>
>>1) Is to simply add (by hand) an extra mond-force whilst allowing GR to
>>continue warping spacetime in the usual way. Obviously you may want to
>>include the pressure due to the mond-force. I would expect this to be
>>'relatively simple'.
>
>I can't think of a way to do this that doesn't make me feel nauseated.
Tsk!
>The equations of general relativity hold in any coordinate system.
>But you can't throw in an extra sort of "MOND-force" in a coordinate-free
>way, since this force acts instantaneously at a distance, and you need
>to pick coordinates to define what "instantaneous" means. This is why
>Einstein threw out Newtonian gravity after he came up with special
>relativity.
Ohh, I'm sure you could get round that to a first approximation.
After all it's virtually newtonian for the last few billion years.
>In theory, I could hold my nose and say "I'll take this one
>special sort of solution of Einstein's equations, the Friedman-
>Robertson-Walker big bang solution, where I do have a special
>time coordinate, namely "cosmic time", and I'll use that time
>coordinate to define an extra "MOND-force" which acts instantaneously
>at a distance, and see how this affects things."
Nah. Just see whether the velocities match tolerably well NOW!
>In practice, I just wouldn't have the stomach to do this sort of thing.
Ahh, 'tis old age a-creeping up!
>I suppose some physicists would, and it might actually be worthwhile!
>It can be helpful, sometimes, to do something monstrously ugly that
>you secretly hope is not ultimately correct, just in order to get a
>little insight and maybe some new ideas. I'm just too much a slave
>to elegance to do this here.
<sigh>
>>2) To recast GR to mimic mond. I would expect this to be mindblowingly
>>difficult and wouldn't advise it even for an expert.
>
>I think this is what those 2 papers I cited were trying to do:
>
>Don't throw in an extra "MOND-force" that acts instantaneously at
>a distance. Instead, modify the Lagrangian and thus the field equations
>of general relativity to get something that acts more "MOND-ish"!
>
>You're right that this sounds mindblowingly difficult. But
>it depends in part on how ugly you let the theory be! And
>also how well you want it to work.
Some people seem to have no fear then.
>I get the impression that the 2 theories in question are a bit
>ugly, and nobody knows for sure if they really work -
>i.e., pass all the dozens of experimental tests that GR passes,
>but also act sufficiently MOND-ish.
>
>Someone should study these theories and report back. But it won't
>be me - I have more fun things to do. If I were the Emperor of Physics,
>I'd send out a team of 4 grad students and a professor to explore
>in this direction. But I'm not.
You mean you aren't? Well you should be. I'll vote for you!
>Sociologically, the real problem with these theories is that they
>aren't consequences of any sort of string or membrane theory.
>If they were, you'd have 100 people working on them day and night,
>and huge conferences on the subject.
I am not surprised. However physics is still an experimental science.
I rather approve of this. You get the maths to fit the physics, not the
other way round. Heretical, I know ......
Walter Pedersen.
ba...@galaxy.ucr.edu (John Baez) wrote in message news:<b45v8n$lnu$1...@glue.ucr.edu>...
Proffessor Baez.
I understand that gravity bends stars,plants,etc together. and dark
energy tugs on the fabric of space and time pushing them apart.
Question: What exactley is dark energy and how is it's property's
formed.
Regards.
W.Pedersen.
John Baez
robert bristow-johnson <r...@surfglobal.net> wrote:
>In article b45v8n$lnu$1...@glue.ucr.edu, John Baez at ba...@galaxy.ucr.edu
>> Eh? I don't know about that! All I know is that dark energy
>> (i.e. a positive cosmological constant) is currently the most
>> conservative way to explain the apparent acceleration in the
>> expansion of the universe.
>John (or anyone else), can you comment more on this?
If you insist.
>i had always been disturbed by the apparently fully accepted finding
>that the rate of expansion of the universe is increasing in time.
>this "dark energy" thing can explain it a bit *for*now*, but doesn't
>the conservation of energy and mass (or the sum of the two when the
>appropriate scalar, c^2, is used to convert between them) still apply
>to our universe, if considered to be a closed system?
No, it doesn't - and this has nothing in particular to do with
"dark energy", either. The quick answer to your question is
that conservation of energy breaks down in general relativity,
except in certain special situations which don't include the most
realistic models of our universe. If I said much more I would
wind up rewriting the FAQ:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html
so you should probably start by reading that.
John Baez
Walter Pedersen <sno...@rogers.com> wrote something like:
> What exactly is dark energy and how are its properties formed?
Einstein's theory of gravity says it's possible that seemingly empty
space has energy in it... together with negative pressure, in a certain
precise proportion. This is called "dark energy". The theory doesn't
require that dark energy exists, and it doesn't say how much of it there
should be, and it doesn't say why it exists if it does. But, if you
assume there is a certain amount of dark energy, Einstein's theory of
gravity will let you calculate it's effects.
The main effect of dark energy is that it makes the expansion of the
universe tend to accelerate. (Actually it's the negative pressure
that really does this.) Ordinary matter, on the other hand, makes
the expansion of the universe tend to slow down.
Einstein thought of this possibility and called the density of dark
energy the "cosmological constant". The term "dark energy" is newer,
and due to Michael Turner.
Recent observations suggest that maybe about 70% of the energy in
the universe is dark energy! For a simple introduction to this
subject, try:
http://snap.lbl.gov/brochure/door.html
Murat Ozer
> In article <f2c9a02c.0303...@posting.google.com>,
> Walter Pedersen <sno...@rogers.com> wrote something like:
[unnecessary quoted text deleted]
> > What exactly is dark energy and how are its properties formed?
> Einstein's theory of gravity says it's possible that seemingly empty
> space has energy in it... together with negative pressure, in a certain
> precise proportion. This is called "dark energy".
> Einstein thought of this possibility and called the density of dark
> energy the "cosmological constant".
Actually, the "density of dark energy" and the "cosmological constant"
are two different but related things. The cosmological constant
\lambda is defined as \lambda=(8\pi*G/c^4)*\rho_DE, where G is
Newton's constant,c is the speed of light and \rho_DE is the density
of dark energy. The two become one when units in which 8\pi*G=c=1 are
used. However, according to a conjecture of Feynman we should try to
formulate gravity so that it does not interact with \rho_DE in order
to solve the cosmological constant problem. In this formalism \rho_DE
is as large as it was in the early universe but \lambda =0 because
(8\pi*G/c^4) is not fused to \rho_DE. One immediate outcome of this
formalism is that the accelerated expansion of the universe is not due
to \lambda but some other mechanism.
Murat Ozer
eb...@lfa221051.richmond.edu
>Einstein thought of this possibility and called the density of dark
>energy the "cosmological constant". The term "dark energy" is newer,
>and due to Michael Turner.
I just want to point out that there is a distinction between these
two terms: "dark energy" is a more general term, meant to encompass
any sort of "stuff" that contributes both energy density and
negative pressure to the Universe, in such a way as to explain
the observations of accelerating expansion.
The cosmological constant is a specific form of dark energy;
the dark energy might be a cosmological constant, or it might
be something more complicated.
John Baez
Oz <ozac...@despammed.com> wrote:
>John Baez <ba...@galaxy.ucr.edu> writes:
>>The equations of general relativity hold in any coordinate system.
>>But you can't throw in an extra sort of "MOND-force" in a coordinate-free
>>way, since this force acts instantaneously at a distance, and you need
>>to pick coordinates to define what "instantaneous" means. This is why
>>Einstein threw out Newtonian gravity after he came up with special
>>relativity.
>Ohh, I'm sure you could get round that to a first approximation.
>
>After all it's virtually newtonian for the last few billion years.
Eh? It's true that within a small patch of spacetime, Newtonian gravity
is a decent approximation. But don't forget, we are talking about
*cosmology* right now, not a little patch of spacetime. I could be
wrong, but I don't think "Newtonian cosmology" comes close to fitting
the data... so I don't think we can just tweak that and get some sort
of reasonable "MOND cosmology". I think we'd really need to combine
general relativity and MOND ideas to develop a "MOND cosmology".
This is the best way I can think of doing it:
>>In theory, I could hold my nose and say "I'll take this one
>>special sort of solution of Einstein's equations, the Friedman-
>>Robertson-Walker big bang solution, where I do have a special
>>time coordinate, namely "cosmic time", and I'll use that time
>>coordinate to define an extra "MOND-force" which acts instantaneously
>>at a distance, and see how this affects things."
It's ugly but I don't think it would be too hard to do.
To which you reply:
>Nah. Just see whether the velocities match tolerably well NOW!
Huh? This doesn't make any sense to me. We're talking about cosmology
here, not the current-day dynamics of galactic clusters. I was
trying to flesh out your vague proposal of building some sort of "MOND
cosmology" to compare to the standard GR-based cosmology. So, I
sketched how to cook up a modified big bang model which incorporates
some MOND idea. To test this model, we'd need to see what it predicts
about cosmology. Cosmology doesn't involve measuring velocities "now"
(whatever that means); it involves peering back many billions of years
and looking at things like redshifts of distant, old galaxies, or the
cosmic microwave background radiation.
Anyway, about working out the details of the "MOND cosmology" I sketched...
>>In practice, I just wouldn't have the stomach to do this sort of thing.
>Ahh, 'tis old age a-creeping up!
No, I *never* would have had the stomach for it. That's why I got
a math PhD instead of a physics PhD.
John Baez
<eb...@lfa221051.richmond.edu> wrote:
>In article <b51383$ssr$1...@glue.ucr.edu>, John Baez <ba...@galaxy.ucr.edu> wrote:
>>Einstein thought of this possibility and called the density of dark
>>energy the "cosmological constant". The term "dark energy" is newer,
>>and due to Michael Turner.
>The cosmological constant is a specific form of dark energy;
>the dark energy might be a cosmological constant, or it might
>be something more complicated.
That's a good point. A positive cosmological constant produces a
positive energy density and negative pressure that are constant
throughout spacetime; fancier forms of dark matter can produce
an energy density and pressure that vary from point to point.
My feeble excuse for glossing over this issue is that:
1) I wanted to keep things simple, and
2) I believe that when newspapers say things like "65% of the
energy density in the universe is dark energy", they are almost
always basing these figures on models where the dark energy is
treated as a cosmological constant, rather than something fancier
that varies from point to point.
I hope I'm right about 2). I know that fancier models of dark
energy have been studied - relevant buzzwords being "tracker
models" and "quintessence" - but I don't think people routinely
use these when trying to estimate basic cosmological parameters.
Ilja Schmelzer
> Question: What exactley is dark energy and how is it's property's
> formed.
The Einstein equations are G_ij = T_ij.
You observe G_ij^obs and T_ij^obs. Unfortunately they don't coinside.
You define T_ij^dark = G_ij^obs - T_ij^obs, and obtain (by definition)
G_ij = T_ij = T_ij^obs + T_ij^dark.
Now you consider the properties of T_ij^dark. From Bianchi identities
nabla G_ij=0 and "local energy-momentum conservation" nabla T_ij^obs
=0 you obtain tautologically "local energy-momentum conservation"
nabla T_ij^dark =0.
Then there is another class of properties of matter, named energy
conditions. If (some part of) T_ij^dark fulfills the energy
conditions typical for of usual matter, you name (this part of)
T_ij^dark "dark matter". If not, you name it (the remaining part)
"dark energy".
Ilja
--
I. Schmelzer, <il...@ilja-schmelzer.net>, http://ilja-schmelzer.net
Oz
>Eh? It's true that within a small patch of spacetime, Newtonian gravity
>is a decent approximation. But don't forget, we are talking about
>*cosmology* right now, not a little patch of spacetime.
I bow to your superior judgement, as ever.
I rather hoped that the recent evolution of a galaxy cluster would be
roughly newtonian to first order. After all I just want the current
rotation curves in this little patch of space.
John Baez
>John Baez <ba...@galaxy.ucr.edu> writes:
>>Eh? It's true that within a small patch of spacetime, Newtonian gravity
>>is a decent approximation. But don't forget, we are talking about
>>*cosmology* right now, not a little patch of spacetime.
>I bow to your superior judgement, as ever.
Grrr... whenever you say something like that, I know trouble is brewing!
>I rather hoped that the recent evolution of a galaxy cluster would be
>roughly newtonian to first order.
Grrr... of course it is, that's what I just SAID. But we're
talking about *cosmology* now, not puny little things like galactic
clusters. Cosmology is the study of the *whole universe*!
>After all I just want the current rotation curves in this
little patch of space.
[Rips out hair in frustration.]
If we're just talking about the recent evolution of a puny little thing
that's moving slowly and ain't too heavy, like a galactic cluster,
then right, we don't need general relativity. Newtonian gravity will
suffice... and so will MOND.
This is precisely what MOND was designed for!
But in the remark which started the current discussion, you asked
whether we could use MOND to develop a *modified big bang model*.
For this, MOND is *not* enough, just as Newtonian gravity was not enough.
The universe is *really big*, so spacetime curvature becomes very important.
So, for full-fledged cosmology, we would need a synthesis of MOND and
general relativity.
Here, I'll remind you:
You wrote:
>Another test would calculate (roughly) the 'mond' age of the universe
>because mond uses a different force law, although currently matched by
>dark matter in conventional models.
Ted replied:
>As far as I know, there is simply no way to
>generate a MOND prediction for the age of the Universe. There is no
>MOND version of the Friedmann equation (the equation that describes
>the way the expansion rate evolves over time), because the Friedmann
>equation is based on general relativity. MOND is inconsistent
>with general relativity and doesn't replace it with anything else.
>The same problem arises with nearly all cosmological observables.
Maybe your confusion, Oz is that you think Ted's "cosmological observables"
include rotation curves of puny things like galactic clusters? No.
He's talking about things like the age of the universe, the redshift-
distance relation for galaxies, the microwave background radiation, and
so on - stuff that involves the whole universe. Here's where MOND has
nothing to say. Here's where we'd need to blend it with GR somehow.
Oz
>In article <b5arkc$1ap$1...@panther.uwo.ca>, Oz <ozac...@despammed.com> wrote:
>>John Baez <ba...@galaxy.ucr.edu> writes:
>>>Eh? It's true that within a small patch of spacetime, Newtonian gravity
>>>is a decent approximation. But don't forget, we are talking about
>>>*cosmology* right now, not a little patch of spacetime.
>>I bow to your superior judgement, as ever.
>Grrr... whenever you say something like that, I know trouble is brewing!
>>I rather hoped that the recent evolution of a galaxy cluster would be
>>roughly newtonian to first order.
>Grrr... of course it is, that's what I just SAID. But we're
>talking about *cosmology* now, not puny little things like galactic
>clusters. Cosmology is the study of the *whole universe*!
Hey Mr Wiz, sir.
*You* might have been talking about the whole universe, after all I
doubt you would notice anything smaller, but I am happy with galactic
clusters for the moment.
>>After all I just want the current rotation curves in this
>>little patch of space.
>[Rips out hair in frustration.]
>
>If we're just talking about the recent evolution of a puny little thing
>that's moving slowly and ain't too heavy, like a galactic cluster,
>then right, we don't need general relativity. Newtonian gravity will
>suffice... and so will MOND.
Eh? Does mond fit the data for clusters?
>This is precisely what MOND was designed for!
So does it fit or don't we know?
>But in the remark which started the current discussion, you asked
>whether we could use MOND to develop a *modified big bang model*.
Um, er, did I? Ahh, yes, perhaps I did.
So the answer is 'no', then, I guess .....
[Oz is impressed with himself. Slowly recovering disc has allowed
contiguous thought trains running into seconds...]
Oz
>In article <b5arkc$1ap$1...@panther.uwo.ca>, Oz <ozac...@despammed.com> wrote:
>
>>John Baez <ba...@galaxy.ucr.edu> writes:
>
>>>Eh? It's true that within a small patch of spacetime, Newtonian gravity
>>>is a decent approximation. But don't forget, we are talking about
>>>*cosmology* right now, not a little patch of spacetime.
>
>>I bow to your superior judgement, as ever.
>
>Grrr... whenever you say something like that, I know trouble is brewing!
>
>>I rather hoped that the recent evolution of a galaxy cluster would be
>>roughly newtonian to first order.
>
>Grrr... of course it is, that's what I just SAID. But we're
>talking about *cosmology* now, not puny little things like galactic
>clusters. Cosmology is the study of the *whole universe*!
Hey Mr Wiz, sir.
*You* might have been talking about the whole universe, after all I
doubt you would notice anything smaller, but I am happy with galactic
clusters for the moment.
>>After all I just want the current rotation curves in this
>little patch of space.
>
>[Rips out hair in frustration.]
>
>If we're just talking about the recent evolution of a puny little thing
>that's moving slowly and ain't too heavy, like a galactic cluster,
>then right, we don't need general relativity. Newtonian gravity will
>suffice... and so will MOND.
Eh? Does mond fit the data for clusters?
>This is precisely what MOND was designed for!
So does it fit or don't we know?
>But in the remark which started the current discussion, you asked
>whether we could use MOND to develop a *modified big bang model*.
Um, er, did I? Ahh, yes, perhaps I did.
So the answer is 'no', then, I guess .....
[Oz is impressed with himself. Slowly recovering disc has allowed
contiguous thought trains running into seconds...]
--
John Baez
[Oz pushes the Wiz's door open on a crack and sticks his nose in.]
>Hey Mr Wiz, sir.
[The Wiz looks up from his calculations, annoyed at the distraction:]
Yeah? What do you want? Still going on about that MOND business?
>*You* might have been talking about the whole universe, after all I
>doubt you would notice anything smaller, but I am happy with galactic
>clusters for the moment.
Oh yeah? I got interested in your conversation when you said:
Another test would calculate (roughly) the 'mond' age of the universe
because mond uses a different force law, although currently matched by
dark matter in conventional models.
This is *not* about the motion of galactic clusters. This is
a truly large-scale issue, where GR effects are very important...
which is why I started talking about blending MOND and general
relativity. To me that's where things get interesting: when we
go past curve-fitting and try to build a new theory of gravity.
But anyway - okay, now you want to forget about that and
talk about galactic clusters!
>Does mond fit the data for clusters?
This is precisely what MOND was designed for!
>So does it fit or don't we know?
According to Milgrom it fits. Click on the graph in Figure 2 here:
http://nedwww.ipac.caltech.edu/level5/Sept01/Milgrom/Milgrom2.html
But like I said, this should not be surprising:
as far as I know, he basically invented MOND by
fitting a curve to this sort of data!
However, you'll notice that the "X-ray cluster cores" are way
off. Some (all?) galactic clusters have lots of hot X-ray
emitting gas near the middle. This was not known when MOND
was invented, and I believe the behavior of these "X-ray cluster
cores" is often touted as the death-blow to MOND. Here is
Milgrom's attempt to fight back:
http://nedwww.ipac.caltech.edu/level5/Sept01/Milgrom/Milgrom2_1.html
In fact, the whole website is worth reading if you're interested
in MOND. And it's not like I'm an expert on this stuff: I just
typed "galactic cluster" and "MOND" into Google when you asked me
this question! So why don't you read this stuff and let me get
back to work?
[The Wiz stretches his leg out and pushes the door shut with
his foot.]
>Ouch!
Gordon D. Pusch
ba...@galaxy.ucr.edu (John Baez) writes:
> I think this is what those 2 papers I cited were trying to do:
Which papers? This appears to be your first posting in this thread?
> Don't throw in an extra "MOND-force" that acts instantaneously at
> a distance. Instead, modify the Lagrangian and thus the field equations
> of general relativity to get something that acts more "MOND-ish"!
Milgrom himself has attempted this, with very little success. In one of his
latter papers, <http://www.arXiv.org/abs/astro-ph/0207231>, he attempts to
argue that both GR and MOND are merely "effective theories" that hold in
different limits --- a claim that I find very deeply unsatisfying.
Milgrom also somewhat schizophrenically argues in that same paper that
MOND might instead be due to a "modified inertia" rather than modified
gravitation, that would make particles obey integral rather than
differential equations of motion, i.e., the EOM would become "nonlocal
in time." I personally find this latter proposal even more repugnant
than modified gravity, and even Milgrom admits that it is hard to see
how such a theory of "modified inertia" could be quantized...
> Sociologically, the real problem with these theories is that they
> aren't consequences of any sort of string or membrane theory.
> If they were, you'd have 100 people working on them day and night,
> and huge conferences on the subject.
Milgrom attempts to put forth a "brane" model of MOND in the aforementioned
paper. Like all attempts at constructing a MOND, it is surpassingly ugly...
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
John Baez
In article <givfxpy...@pusch.xnet.com>,
Gordon D. Pusch <gdp...@NO.xnet.SPAM.com> wrote:
>ba...@galaxy.ucr.edu (John Baez) writes:
>> I think this is what those 2 papers I cited were trying to do [...]
>Which papers?
1988, Physics Letters B202, 497
Jacob D. Bekenstein
Phase Coupled Gravitation and Gauge Fields
1997, ApJ, 480, 492
Sanders, R. H.
A Stratified Framework for Scalar-Tensor Theories of Modified Dynamics
http://xxx.lanl.gov/abs/astro-ph/9612099
>This appears to be your first posting in this thread?
No:
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&safe=off&selm=b48qeg%24pjv%241%40glue.ucr.edu
Phillip Helbig (remove CLOTHES to reply)
> 1997, ApJ, 480, 492
> Sanders, R. H.
> A Stratified Framework for Scalar-Tensor Theories of Modified Dynamics
> http://xxx.lanl.gov/abs/astro-ph/9612099
I spent a couple of years at the Kapteyn Institute in Groningen where
Bob Sanders is a professor. ONE of the things he works on is MOND. In
the last MOND talk I heard him give, he mentioned that the theory in
this paper is no longer tenable. Bob wrote a review article in ANNUAL
REVIEWS OF ASTRONOMY AND ASTROPHYSICS which appeared about a year or so
ago which brings the reader up to (that) date.